Some characterizations of compact Einstein-type manifolds

Abstract

In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate, as consequence we obtain under certain hypotheses that the Hawking mass is bounded from bellow in terms of area. Then we give a topological classification for its boundary. Finally, we prove a gap result for a compact Einstein-type manifold with boundary.

Geometry of static perfect fluid space-time

“…A similar result was established for quasi-Einstein manifolds by Diógenes et al [19]. In another direction, inspired by ideas outlined in [16], Andrade and Melo [2] proved recently that, under suitable conditions, the Hawking mass of Einstein-type manifolds is bounded from below by the area of the boundary.…”